## Quasiclassical Theory for Dirac Material/Superconductor Proximity Structures

##### Master thesis

##### Permanent lenke

http://hdl.handle.net/11250/2615565##### Utgivelsesdato

2016##### Metadata

Vis full innførsel##### Samlinger

- Institutt for fysikk [1809]

##### Sammendrag

In the decade since the experimental discovery of graphene and the topological insulators, the field of Dirac materials, a new class of materials with linear low-energy dispersions, has attracted great research interest. Some of this research is focused on the possibility of new physical phenomena arising when coupling superconductors to Dirac materials. The quasiclassical theory of superconductivity has been used with success to describe various phenomena arising when coupling superconductors to \eg non-Dirac normal and ferromagnetic materials. In this thesis, we expand the quasiclassical theory by first deriving the Eilenberger equation valid for Dirac materials with spin-momentum locking. In 2D materials, focusing on the particle transport on the 1D edge, we show that in the high-impurity limit the self-energies for non-magnetic potentials completely drop out of the resulting equations, leading to a simplified Eilenberger equation. In the 3D case with transport on a 2D surface we derive the Usadel equation valid in the diffusive limit. In both high-impurity equations, the most significant difference from the non-Dirac equations is the fact that the exchange energy enters in the same way as the vector potential, hence altering the way exchange fields affect such systems.
In order to expose how exchange fields affect diffusive Dirac materials with spin-momentum locking, we study superconductor/normal metal (S|N), superconductor/ferromagnet (S|F), superconductor/normal metal/superconductor (S|N|S) and superconductor/ferromagnet/superconductor (S|F|S) structures both in and out of equilibrium. Analysing the systems both analytically and numerically, we investigate how exchange fields affect the penetration of Cooper pairs into Dirac materials and influences physical observables such as the density of states, differential conductance and charge current. We find that the direction of the exchange field greatly alters the effect on the systems, where fields parallel to the transport direction lead to an additional phase in the system, while only fields normal to the transport direction lead to attenuation of Cooper pairs, leading to a Cooper pair penetration length depending only on the normal fields, $\xi_F \sim |v_\mathrm{F}/\mathbf{h}_{\perp}|$. The phase shift caused by the parallel field components is seen in both the density of states and charge current in S|F|S junctions, allowing \eg for the possibility of tuning the charge current at zero phase difference by changing the strength of the field and the length of the weak link. For an S|N|S junction, the theory also yields results for the current-phase relation in good agreement with recent experimental results.